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The function $f(x)=\left\{\begin{matrix} \frac{|x|}{x}, & if & x≠0\\0, & if & x=0\end{matrix}\right.$ is : |
Continuous at x=0 Discontinuous at x=0 Continuous for all $x \in R$ Discontinuous for all $x \in R$ |
Discontinuous at x=0 |
$f(x)=\left\{\begin{matrix} \frac{|x|}{x}, &x≠0\\0, &x=0\end{matrix}\right.$ $f(x)=\left\{\begin{matrix}-1, &x<0\\0, &x=0\\1,&x>0\end{matrix}\right.$ so $LHL=-1(x=0),RHL=1(x=0)$ $f(0)=0$ discontinuous at $x=0$ $(f(0)≠LHL≠RHL)$ |
